Mathematics
In the given figure, AB || CD || EF. If AC = 7 cm, AE = 14 cm and BF = 20 cm, then DF is equal to:
7 cm
14 cm
10 cm
16 cm
Mid-point Theorem
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Answer
Given, AB || CD || EF, AC = 7 cm, AE = 14 cm and BF = 20 cm.
Let the length of DF be x cm.
According to equal intercept theorem,
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
From figure,
⇒ AE = AC + CE
⇒ 14 = 7 + CE
⇒ CE = 7 cm.
Since, OA makes equal intercept, so OB will also make equal intercepts.
∴ BD = DF = x (let)
From figure,
⇒ BF = BD + DF
⇒ 20 = x + x
⇒ 2x = 20
⇒ x = = 10 cm.
Hence, option 3 is the correct option.
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